The Dehn functions of Stallings–Bieri groups

@article{Carter2015TheDF,
  title={The Dehn functions of Stallings–Bieri groups},
  author={William Carter and Max Forester},
  journal={Mathematische Annalen},
  year={2015},
  volume={368},
  pages={671-683}
}
We show that the Stallings–Bieri groups, along with certain other Bestvina–Brady groups, have quadratic Dehn function. 

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References

SHOWING 1-10 OF 21 REFERENCES

The Dehn Function of Stallings’ Group

We prove that the Dehn function of a group of Stallings that is finitely presented but not of type $${\mathcal{F}_3}$$ is quadratic.

Doubles, Finiteness Properties of Groups, and Quadratic Isoperimetric Inequalities☆☆☆

Abstract We describe a doubling construction that gives many new examples of groups that satisfy a quadratic isoperimetric inequality. Using this construction, we prove that the presence of a

An isoperimetric function for Bestvina–Brady groups

Given a right‐angled Artin group A, the associated Bestvina–Brady group is defined to be the kernel of the homomorphism A → ℤ that maps each generator in the standard presentation of A to a fixed

Finitely Presented Subgroups of Automatic Groups and their Isoperimetric Functions

We describe a general technique for embedding certain amalgamated products into direct products. This technique provides us with a way of constructing a host of finitely presented subgroups of

The geometry and topology of Coxeter groups

These notes are intended as an introduction to the theory of Coxeter groups. They closely follow my talk in the Lectures on Modern Mathematics Series at the Mathematical Sciences Center in Tsinghua

Filling in solvable groups and in lattices in semisimple groups

The Dehn function of SL(n;Z)

We prove that when n >= 5, the Dehn function of SL(n;Z) is quadratic. The proof involves decomposing a disc in SL(n;R)/SO(n) into triangles of varying sizes. By mapping these triangles into SL(n;Z)

The Geometry of the Word Problem for Finitely Generated Groups

Dehn Functions and Non-Positive Curvature.- The Isoperimetric Spectrum.- Dehn Functions of Subgroups of CAT(0) Groups.- Filling Functions.- Filling Functions.- Relationships Between Filling

Pushing fillings in right‐angled Artin groups

TLDR
The results give sharp bounds on the higher Dehn func- tions of Bestvina-Brady groups, a complete characterization of the divergence of geodesics in RAAGs, and an upper bound for filling loops at infinity in the mapping class group.